In the given figure, L and M are midpoints of two equal chords AB and CD of a circle with centre O.

Prove that:

(i) angle OLM = angleOML

(ii)angle ALM = angle CML

Asked by pereiracalida | 14th Jan, 2018, 06:48: PM

Expert Answer:

 
begin mathsize 16px style Since space straight L space and space straight M space are space the space midpoints space of space chords space AB space and space CD space respectively comma
OL perpendicular AB space and space OM perpendicular CD
But comma space equal space chords space of space straight a space circle space areequidistant space from space the space centre
rightwards double arrow OL equals OM
In space triangle space OLM comma
OL equals OM
rightwards double arrow angle OLM equals angle OML
rightwards double arrow 90 degree minus angle OLM equals 90 degree minus angle OML
rightwards double arrow angle ALO minus angle OLM equals angle CMO minus angle OML
rightwards double arrow angle ALM equals angle CML end style

Answered by Rashmi Khot | 15th Jan, 2018, 11:05: AM